In 2001, Le Bars proved that there exists an existential monadic second-order (EMSO) sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence (even for [Formula: see text]).

中文翻译：

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关于图的短存在单子二阶句子的逻辑规律

2001 年，Le Bars 证明存在一个存在单子二阶 (EMSO) 句子，使得它在 [Formula: see text] 上为真的概率不收敛，并推测对于具有两个一阶变量的 EMSO 句子，零一定律成立。在本文中，我们证明了[公式：见文本]的猜想失败，并给出了变量较少但没有收敛的句子的新示例（即使对于[公式：见文本]）。